Euclidean Bus Mobility and Route Optimization, A Comparison

Routes in Queens, New York City, NY

Introduction

This project uses stplanr transport modeling package to design an optimal transport route for bus or cycle routes in New York City. Stplanr is a transport planning visualization R package that can be used to plan transit networks, in addition to transit planning elements such as identifying transit catchment areas, origin/destination data and ride frequency visualizations, among others. In their white paper, the devlopers of stplanr call for an accountable, transparent and democratized transit planning system that doesn’t rely on proprietary and often vastly different data sources and data processing softwares. Although the package can visualize a whole host of data, this project will focus on comparing direct desire lines or “Euclidean” routes (as the crow flies), existing bus networks and stplanr’s optimized routes. To wit: this can map the efficiency of the bus routes compared to the most direct route possible if there were no built environment factors in the way.

Methods

To adequately compare desire lines, bus routes, and the most efficient routes with the current street network, this project will require at minimum three data sources. Each of these will be sourced separately and overlaid onto each other:

• Data Source: leaflet data for basemap
  • Methods: This can be sourced directly into R by installing the leaflet package. It is an interactive map so the user can navigate it.
    
  • Source: Leaflet for R
• Data Source: OpenStreetMap (OSMR) data for transit data, either bus or cycle routes, this is used as the route vector data.
  • Methods: This can be sourced directly into R, with an overpass query.
    
  • Source: Mapping with OpenStreetMap in R
• Data Source: NYC Open Data for Bus Shelter locations
  Despite significant searching, there is no comprehensive bus stop dataset, so the project will focus on bus stop shelters, which are mapped via NYC Open Data. I used Bus Shelters as there would be thousands upon thousands of bus stops in NYC, and this would be too computationally intensive to process.
  
  • Methods: This is brought into R as a CSV file. Each bus stop shelter has longitude and latitude coordinates that align with leaflet and OpenStreetMap projections.
    
  • Source: NYC Bus Stop Shelters, NYC Transit analysis
• Data Source: NYC Open Data for NYC Borough Boundaries
  • Methods: This is brought into R as a shapefile. This will provide the basemap boundary for NYC to ensure all data is within the city limits, represented on the leaflet map.
  • Source: NYC Borough Boundaries, Department of City Planning

Data Preparation

• Load the necessary R packages for spatial data manipulation and visualization (e.g., ggmap, dplyr, stplanr, osmdata, sf, leaflet).
• Import the NYC basemap shapefile and bus shelter CSV data into R.
• Convert the bus shelter data into an sf object with appropriate coordinate reference system (CRS).

Terms:

• Desire Lines & “Euclidean”: Straight lines connecting origin and destination points, representing the most direct path between them.
• OSRM: Open Street Routing Machine, a routing engine that uses Open Street Map data to calculate routes, shortest routes, travel times, and can be used to make travel time maps, distance routing for car, bike and walking.

Interactive Map:

#install libraries
library(ggmap) #vestigial
library(dplyr) #data manipulation
library(stplanr) #od2line calculation, origin-destination programming
library(osmdata) #open street maps data
library(sf) #spatial data
library(tidyverse) #data manipulation
library(leaflet) #interactive map
library(purrr) #for map2 function
library(kableExtra) #for attractive table formatting
library(scales) #for comma function

#SHAPEFILES AND MAP

bbox <- c(left = -73.96, bottom = 40.54, right = -73.70, top = 40.81)
#create bounding box for NYC

nyc_map <- "data/"#

#nyc basemap, downloaded from nyc open data. source: https://search.r-project.org/CRAN/refmans/ptools/html/nyc_bor.html

nyc_sf <- st_read(nyc_map, quiet =TRUE)
#bring in nyc_map as a sf

shelters_sf <- read_csv("data/Bus_Stop_Shelter_20251020.csv")
#NOTE: REPLACE WITH DATA WHEN USING QUARTO!
#this brings in the bus stop shelter information. source: https://data.cityofnewyork.us/Transportation/Bus-Stop-Shelters/qafz-7myz

shelters_sf_fix <- st_as_sf(shelters_sf, coords = c("Longitude","Latitude"), crs = 4326)
#convert to sf object with the correct coordinate reference system

osmdata::set_overpass_url("https://overpass-api.de/api/interpreter")
#set overpass url for open street maps, finds specific data package, the below query will use this

osm_data <- opq(bbox = bbox) %>%
  add_osm_feature(key = "highway", value = c("primary","secondary")) %>%
  osmdata_sf()
#import data for primary and secondary highways from open street maps
#opq is overpass query, which is basically where you want to look

# STPLANR FUNCTIONS

shelters_sf_fix <- shelters_sf_fix %>%
  mutate(id = paste0("S", row_number()))
#add ID column for origin-destination pairs so they have a corresponding number

flow_all <- expand.grid(o = shelters_sf_fix$id, #create origin
                        d = shelters_sf_fix$id, #create destination
                        stringsAsFactors = FALSE) %>% #make sure they aren't factors
  filter(o != d) %>% # this remove self-pairs so O is not D
  mutate(trips = 1) %>% #add trip count of 1 for each pair
  sample_n(50) #sample 50 random paris to avoid blowing up the computer

desire_lines_all <- od2line(flow_all, zones = shelters_sf_fix, zone_code = "id") #use od2line function to create desire lines (euclidean) for all pairs

shelter_coords <- shelters_sf_fix %>%
  st_coordinates() %>%
  as.data.frame() %>%
  bind_cols(id = shelters_sf_fix$id)
#extract coordinates and bind with ID column

route_single <- function(o_id, d_id) { #function to create a single route between origin and destination
  o <- shelter_coords %>% filter(id == o_id) 
  #filter to get origin coordinates
  d <- shelter_coords %>% filter(id == d_id)
  #filter to get destination coordinates

  r <- try(route_osrm(from = c(o$X, o$Y),
                      to   = c(d$X, d$Y)), silent = TRUE)
#use try to catch errors  (e.g., no route found)
  if (inherits(r, "try-error")) return(NULL)
#if route found, return the route
  return(r)
}

routes_list <- purrr::map2(flow_all$o, flow_all$d, route_single)
#create routes for all origin-destination pairs using the route_single function
routes_list <- routes_list[!sapply(routes_list, is.null)]
#remove any NULL results (failed routes)
routes_sf <- do.call(rbind, routes_list)
#combine all routes into a single sf object

#ROUTE & DESIRE LENGTH CALCULATION, MEAN & PCT CHANGE

routes_projection <- st_transform(routes_sf, 32618)
desire_projection <- st_transform(desire_lines_all, 32618)
#ensures the correct, projected shapefile for computation not mapping

route_length <- st_length(routes_projection)
desire_length <- st_length(desire_projection)
#compute lengths

route_length <- as.numeric(route_length)
desire_length <- as.numeric(desire_length)
#convert lengths to numeric values

lengths_tbl <- tibble(
  route_m  = route_length,
  desire_m = desire_length,
  origin = flow_all$o,
  destination = flow_all$d
)
#create tibble to compare lengths in the final map w/ IDs

lengths_tbl_print <- tibble(
  route_m  = comma(round(route_length)),
  desire_m = comma(round(desire_length)),
  origin = flow_all$o,
  destination = flow_all$d
)
#tidy data for later printing in a kable

mean_route <- mean(route_length, na.rm = TRUE)
mean_desire <- mean(desire_length, na.rm = TRUE)
#calculate means for both route and desire lengths

percent_change <- ((mean_route - mean_desire) / mean_desire) * 100
#calculate percent change 

mean_lengths <- data.frame(
  type = c("Route Length", "Desire Line Length"),
  mean_length_m = c(round(mean_route), round(mean_desire)))

#put these into a data frame, rounded to whole numbers


mean_lengths <- mean_lengths %>%
  mutate(
    mean_length_km = mean_length_m / 1000,
    percent_change = c(percent_change, NA)
  )
#add km conversion and percent change to the data frame, i converted to KM for ease of computation (ie: dividing by 1,000)

mean_lengths_print <- mean_lengths %>%
  mutate(
    mean_length_km = comma(round(mean_length_m / 1000)),
    percent_change = comma(round(percent_change))
  )
#tidy data for later printing in a kable

#LEAFLET PREP

nyc_leaflet  <- st_transform(nyc_sf, 4326)
roads_leaflet <- st_transform(osm_data$osm_lines, 4326)
desire_leaflet <- st_transform(desire_lines_all, 4326)
routes_leaflet <- st_transform(routes_sf, 4326)
#transform all data to WGS84 for leaflet mapping

desire_leaflet_popup <- paste0(
  "<b>Desire Line</b><br/>",
  "Origin: ", desire_leaflet$o, "<br/>",
  "Destination: ", desire_leaflet$d, "<br/>",
  "Desire Line Distance: ", round(lengths_tbl$desire_m / 1000), " km"
)
#create popup info for desire lines for interactive map
  
routes_leaflet_popup <- paste0(
  "<b>OSRM Route</b><br/>",
  "Origin: ", desire_leaflet$o, "<br/>",
  "Destination: ", desire_leaflet$d, "<br/>",
  "Route Distance: ", round(lengths_tbl$route_m / 1000), " km<br/>"
)
#create popup info for routes for interactive map

pal_desire <- colorNumeric(
  palette = "viridis",
  domain  = lengths_tbl$desire_m
)
#create color palette for desire lines based on distance

pal_routes <- colorNumeric(
  palette = "inferno",
  domain  = lengths_tbl$route_m
)
#create color palette for routes based on distance

selected_ids <- unique(c(flow_all$o, flow_all$d))
#get unique IDs of sampled shelters

selected_shelters <- shelters_sf_fix %>% 
  filter(id %in% selected_ids)
#filter shelters to only those that were sampled

#LEAFLET MAP

leaflet() %>%
  addProviderTiles("CartoDB.Positron") %>%
  
  addPolygons(data = nyc_leaflet,
              color = "black", weight = 3,
              fillOpacity = 0.1,
              group = "NYC Boundary") %>%
  # Add OSM roads w/ positron background
  
  addPolylines(
    data = desire_leaflet,
    color = pal_desire(lengths_tbl$desire_m),
    weight = 3,
    opacity = 0.7,
    popup = desire_leaflet_popup,
    group = "Desire Lines"
  ) %>%
  
  addPolylines(
    data = routes_leaflet,
    color = pal_routes(lengths_tbl$route_m),
    weight = 3,
    opacity = 0.8,
    popup = routes_leaflet_popup,
    group = "OSRM Routes"
  ) %>%
  
  addLegend(
    pal = pal_desire,
    values = lengths_tbl$desire_m,
    title = "Desire Line Distance (m)",
    position = "bottomright",
    group = "Desire Lines"
  ) %>%
  #add a legend for desire lines
  addLegend(
    pal = pal_routes,
    values = lengths_tbl$route_m,
    title = "OSRM Route Distance (m)",
    position = "bottomleft",
    group = "OSRM Routes"
  ) %>%
  #add a legend for osrm routes

    addCircleMarkers(data = shelters_sf_fix,
                   color = "blue",
                   radius = 1,
                   popup = ~id,
                   group = "Bus Shelters") %>%
  #add all bus shelters
  addCircleMarkers(
    data = selected_shelters,
    color = "purple",
    radius = 6,
    fillOpacity = 0.9,
    group = "Sampled Shelters"
  ) %>%
  #add sampled bus shelters with purple markers
  addLayersControl(
    overlayGroups = c("NYC Boundary", "Sampled Shelters",
                      "Desire Lines", "OSRM Routes",
                      "Bus Shelters"),
    options = layersControlOptions(collapsed = FALSE)
  )

Tables:

mean_lengths_print %>%
  kable(col.names = c("Type", "Mean Length (m)", "Mean Length (km)", "Percent Change (%)"),
        caption = "Mean Lengths of OSRM Routes vs Desire Lines") %>%
  kable_styling(full_width = FALSE, position = "left")

Mean Lengths of OSRM Routes vs Desire Lines

Type	Mean Length (m)	Mean Length (km)	Percent Change (%)
Route Length	18690	19	26
Desire Line Length	14795	15	NA

lengths_tbl_print %>%
  kable(col.names = c("Route Length (m)", "Desire Line Length (m)", "Origin ID", "Destination ID"),
        caption = "Comparison of Route Lengths and Desire Line Lengths for Sampled Origin-Destination Pairs") %>%
  kable_styling(full_width = FALSE, position = "left")

Comparison of Route Lengths and Desire Line Lengths for Sampled Origin-Destination Pairs

Route Length (m)	Desire Line Length (m)	Origin ID	Destination ID
30,257	23,200	S2654	S3350
27,297	10,416	S2911	S500
5,421	4,736	S3007	S2672
8,141	7,533	S1715	S1644
40,923	36,446	S718	S1053
23,396	20,371	S350	S951
29,365	24,216	S228	S1381
2,004	1,435	S1831	S1499
23,234	19,917	S2130	S1119
36,804	29,524	S3321	S2653
19,096	17,677	S391	S2477
12,553	11,606	S3107	S552
21,470	16,176	S796	S1429
18,890	16,231	S566	S1355
4,783	3,829	S2247	S2573
20,348	4,790	S2528	S1149
29,169	14,003	S440	S3299
21,501	17,324	S835	S3049
10,958	9,511	S2712	S536
25,270	22,048	S554	S1397
16,289	13,562	S1059	S1697
11,256	8,667	S1483	S659
25,692	19,732	S2596	S2454
22,969	8,897	S1143	S3018
21,156	18,881	S387	S1995
6,654	4,242	S846	S1420
14,785	13,102	S125	S2636
27,103	15,865	S3208	S476
28,189	24,865	S3366	S2710
29,990	27,296	S3353	S1875
17,053	15,383	S1552	S319
37,323	30,443	S1057	S2838
3,669	3,087	S792	S17
3,496	3,392	S1654	S2042
21,786	19,635	S2985	S1951
8,926	7,514	S419	S444
7,397	6,491	S125	S679
6,583	6,126	S2508	S3172
11,243	8,611	S2054	S2368
22,268	18,055	S961	S2870
1,573	1,440	S239	S414
23,476	19,400	S943	S615
14,462	12,241	S2795	S2807
9,039	8,196	S1904	S1528
5,957	4,983	S1534	S1357
16,914	11,964	S2454	S3009
35,736	31,778	S3230	S1027
26,887	22,348	S1243	S554
23,967	22,041	S1023	S333
21,775	20,500	S3293	S1290

Results

The mean route length for the optimized routes for this particular sample run is 18.69 km, while the mean Euclidean desire line length is 14.79 km. This represents a percent change of 26.33% longer for the optimized routes compared to the direct desire lines. The interactive map above visualizes these routes, with desire lines colored based on their lengths and Open Street Routing Machine (OSRM) routes similarly colored with a different theme.

Discussion

The results indicate that the optimized OSRM routes are significantly longer than the direct desire lines, which is generally expected given the constraints of the built environment and road network. The percent change of 26.33% suggests that while the desire lines represent the most direct path between two points, real-world travel must navigate around obstacles, follow roadways, and adhere to traffic regulations etc.

Limitations

• This does not represent all bus stops in NYC, just shelters. Although the exact number of bus stops is difficult to find, the MTA states that there are 327 bus routes in the five boroughs and countless stops in between. To make the data manageable both in computation and visualization, this study only selects 50 at random. This limits the amount of data points and does not fully capture the bus network.
• The OSRM routing service may not always find a route between two points, especially if they are very close together or in areas with limited road connectivity. The code removes these unroutable routes, and they are not shown in the data.
• The analysis does not account for real-world factors such as traffic, hazards, closures, road conditions, bus “bunching” or transit schedules, which can significantly impact actual travel times and route efficiency.The analysis assumes that the shortest path is the most efficient, which may not always be the case in real-world scenarios.
• The sample size of 50 origin-destination pairs is relatively small and is not be representative of the entire bus network in NYC.
• Only “Primary” and “Secondary” roads are sampled here, as the computation for the smaller roads (tertiary etc.) was too processing heavy. This eliminates a large selection of routes.

Future:

Future research could expand the sample size to include more origin-destination pairs, or even all bus stops. Incorporating real-world travel time data, traffic patterns, and transit schedules could provide a more comprehensive understanding of route efficiency. Further analysis could also explore the impact of different modes of transportation, such as cycling or walking, on route optimization and efficiency.

References

• A. J. Smit. Mapping with Google in R. Source.
• CRAN. stplanr Paper and Vignettes. Source.
• NYC Open Data. Bus Stop Shelters Dataset. Source.
• Robin Lovelace. stplanr: R Package Documentation. Source.
• openstreetmap.de. OpenStreetMap Routing Service. Source.
• RStudio. Leaflet for R. Source.
• MTA. New York City Transit Subway and Bus Facts 2019. Source.
• NYC.gov. NYC Borough Boundaries Dataset. Source.